Fitted Values from an hbb_fit

Computes observation-level fitted values from the posterior means of the fixed effects (and state random effects for SVC models).

Usage

# S3 method for class 'hbb_fit'
fitted(object, type = c("response", "extensive", "intensive"), ...)

Arguments

object: An object of class "hbb_fit" returned by hbb.
type: Character string: "response" (default), "extensive", or "intensive".
...: Currently unused; included for S3 method consistency.

Value

Numeric vector of length $N$.

Details

Three types are available:

"response": (Default.) The predicted enrollment proportion $\hat{q}_i \cdot \hat{\mu}_i$, i.e. the probability of a positive enrollment times the conditional enrollment share. All values lie in $[0, 1]$.
"extensive": The predicted participation probability $\hat{q}_i = \mathrm{logistic}(X_i' \hat\alpha)$.
"intensive": The predicted conditional enrollment share $\hat\mu_i = \mathrm{logistic}(X_i' \hat\beta)$.

SVC adjustment

For state-varying coefficient models (model_type %in% c("svc", "svc_weighted")), the linear predictors include state-level random effects: $$ \eta_{\mathrm{ext},i} = X_i' \hat\alpha + X_i' \hat\delta_{\mathrm{ext}}[s(i)], $$ where $\hat\delta$ is the posterior mean of the state random effects extracted via .extract_delta_means(). If delta extraction fails, a warning is issued and fitted values use fixed effects only.

Examples

if (FALSE) { # \dontrun{
fit <- hbb(y | trials(n_trial) ~ poverty + urban, data = my_data)
yhat   <- fitted(fit)                      # q * mu (proportion)
q_hat  <- fitted(fit, type = "extensive")  # participation prob
mu_hat <- fitted(fit, type = "intensive")  # conditional share
} # }